Hybrid Optimization Techniques for Solving Twin Support Vector Machines Using ADMM and IPM

Abstract

In this research, we explore the enhancement of a Twin Support Vector Machine (TWSVM) by combining the Alternating Direction Method of Multipliers (ADMM) and the Interior Point Method (IPM). TWSVM is a binary classification method that constructs two non-parallel hyperplanes by solving a pair of quadratic programming problems. To address the sensitivity of TWSVM to noise and outliers, we extend the formulation to a robust variant, incorporating regularization techniques to improve performance in noisy environments, termed the Robust Twin Support Vector Machine (RTWSVM). ADMM is employed to decompose the optimization problem into smaller subproblems, offering computational efficiency for large-scale datasets. Meanwhile, IPM is utilized for its globally convergent properties, ensuring precise optimization even in the presence of complex constraints. In iteration of ADMM, the subproblem involving argmin optimization is solved efficiently using IPM, ensuring both accuracy and rapid convergence. This hybrid approach combines the scalability of ADMM with the optimization precision of IPM. Experimental results demonstrate the computational efficiency and robustness of the proposed method, particularly on large-scale, noisy datasets. The method is evaluated on real-world datasets such as Breast Cancer Wisconsin, Dry Bean, Heart Disease, and Pima Indians Diabetes, offering valuable insights into its practical applications.